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SageMath
E = EllipticCurve("fo1")
E.isogeny_class()
Elliptic curves in class 97344fo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 97344.z4 | 97344fo1 | \([0, 0, 0, 46644, -8260720]\) | \(12167/39\) | \(-35974285014859776\) | \([2]\) | \(688128\) | \(1.8600\) | \(\Gamma_0(N)\)-optimal |
| 97344.z3 | 97344fo2 | \([0, 0, 0, -440076, -96843760]\) | \(10218313/1521\) | \(1402997115579531264\) | \([2, 2]\) | \(1376256\) | \(2.2066\) | |
| 97344.z2 | 97344fo3 | \([0, 0, 0, -1900236, 913002896]\) | \(822656953/85683\) | \(79035504177646927872\) | \([2]\) | \(2752512\) | \(2.5531\) | |
| 97344.z1 | 97344fo4 | \([0, 0, 0, -6767436, -6776004976]\) | \(37159393753/1053\) | \(971305695401213952\) | \([2]\) | \(2752512\) | \(2.5531\) |
Rank
sage: E.rank()
The elliptic curves in class 97344fo have rank \(1\).
Complex multiplication
The elliptic curves in class 97344fo do not have complex multiplication.Modular form 97344.2.a.fo
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
